Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Problem 29

The forces on a small airplane (mass \(1160 \mathrm{kg}\) ) in horizontal flight heading eastward are as follows: gravity \(=16.000 \mathrm{kN}\) downward, lift \(=16.000 \mathrm{kN}\) upward, thrust \(=1.800 \mathrm{kN}\) eastward, and \(\mathrm{drag}=1.400 \mathrm{kN}\) westward. At \(t=0,\) the plane's speed is \(60.0 \mathrm{m} / \mathrm{s} .\) If the forces remain constant, how far does the plane travel in the next \(60.0 \mathrm{s} ?\)

Short Answer

Expert verified
Answer: The airplane travels approximately 4221 meters eastward in 60.0 seconds.

Step by step solution

01

Sum up horizontal forces to find net force

In this problem, we only need to analyze horizontal forces, which are thrust (eastward) and drag (westward). To find the net horizontal force (\(F_{net}\)), subtract the drag force from the thrust force: \(F_{net} = F_{thrust} - F_{drag} = 1800 - 1400 = 400\,\text{N}\).
02

Calculate the airplane's acceleration

Now that we have the net force, we can find the airplane's acceleration using Newton's second law, which states \(F = ma\). Rearrange the formula to solve for acceleration (\(a\)): \(a = \frac{F_{net}}{m} = \frac{400\,\text{N}}{1160\,\text{kg}} \approx 0.345\,\text{m/s}^2\)
03

Use kinematic equations to find the distance traveled

We are given the initial speed (\(v_0 = 60.0\,\text{m/s}\)), time (\(t = 60.0\,\text{s}\)), and acceleration (\(a = 0.345\,\text{m/s}^2\)). We can use the kinematic equation for the distance traveled, which is: $$ d = v_0t + \frac{1}{2}at^2 $$ Plug in the given values and compute the distance: $$ d = (60.0\,\text{m/s})(60.0\,\text{s}) + \frac{1}{2} (0.345\,\text{m/s}^2)(60.0\,\text{s})^2 \approx 3600\,\text{m}+ 621\,\text{m} = 4221\,\text{m} $$
04

Report the final answer

In the next 60.0 seconds, the airplane travels a distance of approximately 4221 meters eastward.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The coefficient of static friction between block \(\mathrm{A}\) and a horizontal floor is 0.45 and the coefficient of static friction between block \(\mathrm{B}\) and the floor is \(0.30 .\) The mass of each block is $2.0 \mathrm{kg}$ and they are connected together by a cord. (a) If a horizontal force \(\overrightarrow{\mathbf{F}}\) pulling on block \(\mathrm{B}\) is slowly increased, in a direction parallel to the connecting cord, until it is barely enough to make the two blocks start moving, what is the magnitude of \(\overrightarrow{\mathbf{F}}\) at the instant that they start to slide? (b) What is the tension in the cord connecting blocks \(A\) and \(B\) at that same instant?
A barge is hauled along a straight-line section of canal by two horses harnessed to tow ropes and walking along the tow paths on either side of the canal. Each horse pulls with a force of \(560 \mathrm{N}\) at an angle of \(15^{\circ}\) with the centerline of the canal. Find the sum of the two forces exerted by the horses on the barge.
A roller coaster is towed up an incline at a steady speed of $0.50 \mathrm{m} / \mathrm{s}$ by a chain parallel to the surface of the incline. The slope is \(3.0 \%,\) which means that the elevation increases by \(3.0 \mathrm{m}\) for every \(100.0 \mathrm{m}\) of horizontal distance. The mass of the roller coaster is \(400.0 \mathrm{kg}\). Ignoring friction, what is the magnitude of the force exerted on the roller coaster by the chain?
Margie, who weighs \(543 \mathrm{N},\) is standing on a bathroom scale that weighs \(45 \mathrm{N}\). (a) With what force does the scale push up on Margie? (b) What is the interaction partner of that force? (c) With what force does the Earth push up on the scale? (d) Identify the interaction partner of that force.
A crate of potatoes of mass \(18.0 \mathrm{kg}\) is on a ramp with angle of incline \(30^{\circ}\) to the horizontal. The coefficients of friction are \(\mu_{\mathrm{s}}=0.75\) and \(\mu_{\mathrm{k}}=0.40 .\) Find the frictional force (magnitude and direction) on the crate if the crate is sliding up the ramp.
See all solutions

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Read Explanation

Astrophysics

Read Explanation

Nuclear Physics

Read Explanation

Solid State Physics

Read Explanation

Electromagnetism

Read Explanation

Space Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free